Question

Расстояния между двумя домами 900м. Из этих домов одновременно на встречу друг другу вышли Саша и Дима. Они встретились через 6 мин. Оказалось, что Саша прошел на 60 м больше, чем Дима. Найдите скорость каждого мальчика. Составьте систему и решите ее способом сложения.

Answer 1

Скорость Саши x м/мин, скорость Димы y м/мин. За 6 мин Саша прошёл 6x м, Дима 6y м. Вместе прошли 900 м. 6x+6y = 900.
Саша прошёл на 60 м больше, чем Дима, то есть 6x-6y = 60.
$\begin{cases}6x+6y=900\\6x-6y=60\end{cases}\Rightarrow\begin{cases}12x=960\\y=x-10\end{cases}\Rightarrow\begin{cases}x=80\\y=70\end{cases}$
Скорость Саши 80 м/мин, Димы - 60 м/мин.

Answer 2

Problem Analysis

We are given that the distance between two houses is 900m. Sasha and Dima start walking towards each other from their respective houses and meet after 6 minutes. It is also given that Sasha walked 60m more than Dima. We need to find the speed of each boy.

Solution

Let's assume that Sasha's speed is x m/min and Dima's speed is y m/min.

We know that Sasha walked 60m more than Dima, so we can write the equation: x = y + 60 (Equation 1)

We also know that Sasha and Dima walked towards each other for 6 minutes and the total distance covered is 900m. So, we can write the equation: 6x + 6y = 900 (Equation 2)

To solve this system of equations, we can use the method of addition.

Solution Steps

1. Substitute the value of x from Equation 1 into Equation 2. 2. Solve the resulting equation to find the value of y. 3. Substitute the value of y into Equation 1 to find the value of x. 4. Calculate the speed of each boy.

Let's solve the equations step by step.

Step 1: Substitute x from Equation 1 into Equation 2

Substituting x = y + 60 into 6x + 6y = 900, we get: 6(y + 60) + 6y = 900

Simplifying the equation: 6y + 360 + 6y = 900 12y + 360 = 900

Step 2: Solve the resulting equation to find the value of y

Subtracting 360 from both sides of the equation: 12y = 900 - 360 12y = 540

Dividing both sides of the equation by 12: y = 540 / 12 y = 45

Step 3: Substitute the value of y into Equation 1

Substituting y = 45 into x = y + 60, we get: x = 45 + 60 x = 105

Step 4: Calculate the speed of each boy

The speed of Sasha is 105 m/min and the speed of Dima is 45 m/min.

Answer

The speed of Sasha is 105 m/min and the speed of Dima is 45 m/min.

Note: The solution assumes that both Sasha and Dima walked at a constant speed throughout the 6 minutes.